adecomp implements the shapley decomposition of changes in a welfare indicator as proposed by Azevedo, Sanfelicce and Minh (2012). Following Barros et al (2006), this method takes advantage of the additivity property of a welfare aggregate to construct a counterfactual unconditional distribution of the welfare aggregate by changing each component at a time to calculate their contribution to the observed changes in poverty and inequality.
Given that the distribution of a observable welfare measure (i.e. income or consumption) for period 0 and period 1 are known, we can construct counterfactual distributions for period 1 by substituting the observed level of the indicators c in period 0, one at a time. For each counterfactual distribution, we can compute the poverty or inequality measures, and interpret those counterfactuals as the poverty or inequality level that would have prevailed in the absence of a change in that indicator.
As much of the micro-decomposition literature, approaches of this nature traditionally suffer from path-dependence (See Essama-Nssah (2012), Fortin et al (2011) and Ferreira (2010) for recent reviews of the literature), in other words, the order in which the cumulative effects are calculated matters . One of the major contributions of Azevedo, Sanfelicce and Minh (2012) is the implementation of the best known remedy for path-dependence which is to calculate the decomposition across all possible paths and then take the average between them. These averages are also known as the Shapley-Shorrocks estimates of each component, implying that we estimate every possible path to decompose these components and then take the average of these estimates (See Shapley (1953) and Shorrocks (1999)).
There is one remaining caveat to this approach: the counterfactual income distributions on which these decompositions suffer from equilibrium-inconsistency. Since we are modifying only one element at a time, the counterfactuals are not the result of an economic equilibrium, but rather a statistical exercise in which we assume that we can in fact modify one factor at a time and keep everything else constant.
For further examples of implementations of this approach please see Azevedo, Inchausete and Sanfelice (2012).
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welfarevar is the welfare aggregate variable.
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components are the components used to construct the welfare variable, and which will be for the decomposition.
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by is the comparison indicator. It must take two categorical values and is usually defines two points in time or two geographic locations, which the difference of the indicator of choice is being decomposed.
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equation() captures the relationship between welfarevar and components. The component variables in varlist must be denoted by c#, and must be separated by an arithmetic operator.
Essama-Nssah, B. (2012). "Identification of Sources of Variation in Poverty Outcomes", World Bank Policy Research Working Papers, No. 5954.
Ferreira Francisco H.G. (2010) "Distributions in Motion: Economic Growth, Inequality and Poverty Dynamics". World Bank Policy Research Working Paper No. 5424. The World Bank, Washington, D.C.
Fortin Nicole, Lemieux Thomas and Firpo Sergio. (2011). "Decomposition Methods in Economics". In: Ashenfelter Orley and Card David (eds) Handbook of Labor Economics, Vol. 4A , pp. 1-102. Northolland, Amsterdam..
Shapley, L. (1953). "A value for n-person games", in: H. W. Kuhn and A. W. Tucker (eds.), Contributions to the Theory of Games, Vol. 2 (Princeton, N.J.: Princeton University Press).
Shorrocks, Anthony (2012) Decomposition procedures for distributional analysis: a unified framework based on the Shapley value. Journal of Economic Inequality (link to publication)
This module should be installed from within Stata by typing "ssc install adecomp". Windows users should not attempt to download these files with a web browser.
Poverty, Inequality, Decomposition, Nonparametric
João Pedro Azevedo
jazevedo@worldbank.org
World Bank
personal page
Minh Cong Nguyen
mnguyen3@worldbank.org
World Bank
Viviane Sanfelice